Last updated: July 31, 2026
Hypotenuse Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
hypotenuse = √(a²+b²), area = ½ab, perimeter = a+b+√(a²+b²), angles = arctan(a/b) and arctan(b/a)
Where:
- a=First leg of the right triangle(length)
- b=Second leg of the right triangle(length)
- c=Hypotenuse(length)
Worked Examples
Classic 3-4-5 triangle
A standard right-triangle example.
- 1Compute hypotenuse = √(3²+4²) = √25 = 5.
- 2Area = ½ × 3 × 4 = 6.
- 3Perimeter = 3 + 4 + 5 = 12.
- 4Angles are arctan(3/4) ≈ 36.869898° and arctan(4/3) ≈ 53.130102°.
Isosceles right triangle
Equal legs create equal acute angles.
- 1Compute hypotenuse = √2 ≈ 1.414214.
- 2Area = ½ × 1 × 1 = 0.5.
- 3Perimeter = 1 + 1 + √2 ≈ 3.414214.
- 4Both acute angles equal 45°.
5-12-13 triangle
A larger Pythagorean triple.
- 1Compute c = √(25 + 144) = 13.
- 2Area = ½ × 5 × 12 = 30.
- 3Perimeter = 5 + 12 + 13 = 30.
- 4Angles are arctan(5/12) and arctan(12/5).
Introduction
The hypotenuse is the defining side of a right triangle. This calculator applies the Pythagorean theorem to two known legs and adds extra geometric outputs like area, perimeter, and the two acute angles.
Pythagorean Theorem Core
Every right triangle with legs a and b and hypotenuse c satisfies c² = a² + b².
Square each leg.
Add the squares.
Take the square root.
The result is always the longest side.
This works only for right triangles.
Area and Perimeter
Once the two legs are known, area and perimeter follow immediately.
Area = ½ab.
Perimeter = a + b + c.
Area uses the perpendicular legs.
Perimeter includes the hypotenuse.
Both outputs use the same input unit system.
Acute Angle Formulas
The remaining two angles are found with inverse tangent ratios.
angleA = arctan(a/b).
angleB = arctan(b/a).
Both angles are acute.
The two angles add to 90°.
Angle output is in degrees.
Input Validation
The calculator requires two positive leg lengths.
legA must be positive.
legB must be positive.
Zero is rejected.
Negative values are rejected.
Invalid inputs return safe zero defaults.
How to Use the Tool
Enter the two legs, calculate, and read the hypotenuse first.
Measure leg a.
Measure leg b.
Enter both positive values.
Review the hypotenuse.
Use area, perimeter, and angles for extra interpretation.
Useful Triangle Triples
Integer triples offer easy manual verification.
3-4-5
5-12-13
8-15-17
7-24-25
9-40-41
Practical Uses
Right-triangle calculations show up in daily geometry and engineering.
Ladder placement
Roof pitch estimates
Coordinate distance checks
Construction layout
Vector magnitude calculations
FAQs
What is a hypotenuse?
It is the side opposite the right angle and always the longest side in a right triangle.
What formula does the calculator use?
It uses c = √(a² + b²) along with derived formulas for area, perimeter, and angles.
Can I enter decimals?
Yes. Any positive finite leg lengths are allowed.
Why do the angles add to 90°?
The three triangle angles sum to 180°, and one angle is already 90°, so the other two must total 90°.
Does the calculator work for non-right triangles?
No. The formulas are specifically for right triangles.
How is angleA defined here?
angleA is computed as arctan(a/b), and angleB as arctan(b/a), matching the implementation used in calculation.ts.
How can I verify a 3-4-5 triangle?
Check that 3² + 4² = 9 + 16 = 25, then take √25 = 5.
What happens with invalid inputs?
The wrapper returns zero-ish outputs plus an error string instead of throwing an exception.